Quiz

Equilibrium temperature profile in a pipe

Laplacian in cylindrical coordinates is

∇²u = (1)/(r)(∂)/(∂r)(r(∂u)/(∂r)) + (1)/(r²)(∂²u)/(∂θ²) + (∂²u)/(∂z²)

Actual plots of log(r ⁄ b) ⁄ log(a ⁄ b):

2.3 1D heat equation with prescribed boundary values, cont'd

From last time:

Plotting solution with Python

(From 0 to 60mph in 20 minutes!)

numpy arrays, broadcasting, outer, linspace, arange, sum, base-0 counting, [1:]

functions (def), for loops

pylab, plot, xlabel, ylabel

Illustration of solution: Jupyter Notebook, HTML

Approximation by lowest-λ solution